Klarinet Archive - Posting 000099.txt from 1997/03

From: Jonathan Cohler <cohler@-----.NET>
Subj: Re: barrels
Date: Mon, 3 Mar 1997 17:45:17 -0500

>On Sun, 2 Mar 1997, James Pyne wrote:
>
>> increasing the bore size raises the pitch while decreasing the bore
>> size lowers the pitch.
>
>Is it possible that this is a typo, or that the two items were
>unintentionally transposed?
>
>If not, and if the above is true, it certainly is a revolutionary musical
>phenomenon. In every other case I know of, increasing the bore size
>_lowers_ the pitch, and vice-versa. For example, opening a bassoon or
>oboe reed increases the bore size and lowers the pitch. Loosening the
>embouchure on saxophone or clarinet allows the reed to open more, thereby
>creating a larger interior volume (among other effects) and lowers the
>pitch.
>
>Ed Lacy
>el2@-----.edu

It's not that simple.

Mr. Pyne is no doubt referring to conical bore shapes of barrels in which
the diameter at one end is larger than the diameter at the other.

On most clarinets, the lower part of the bore (near the bell) is flared out
a bit. This has the effect of raising the frequency of all the wind column
resonance peaks for notes whose fingerings extend into this region.
However, the lower peaks are raised progressively more, with the
fundamental being raised the most. This is why when you blow louder on a
low E it gets noticeably flatter on most clarinets. The higher resonance
peaks, which are flat from the perfect cylinders 3:1, 5:1 ratios pull the
instrument into a slightly flatter "regime of oscillation".

At the other end of the instrument (the mouthpiece/barrel end) a flaring of
the bore has exactly the opposite effect. Namely, all the resonance peaks
are lowered, with the the lowest peaks being lower the most.

This is because the mouthpiece end of the instrument is a pressure antinode
(i.e. there is maximal variation of the air pressure up and down, whereas
the bell end (or open tone hole) is a pressure node (no variation in the
air pressure).

Enlargement of the bore at a pressure antinode lowers the frequency. And
enlargement at a node raises the frequency.

This business of bore flare at the bottom, flare at the top (in the
barrel/mouthpiece) and positioning of the register key are the critical
elements in determining the overall tuning and resonance of a clarinet.

A very complete discussion of this entire issue can be found in Benade's
Fundamentals of Musical Acoustics (Dover).

--------------------
Jonathan Cohler
cohler@-----.net